Comment by peterburkimsher | Hacker News Reader

Comment by peterburkimsher | Hacker News Reader

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peterburkimsher

Tell me more about the difference between "potential infinity" and "actual infinity".

Recursive functions in computer programming, or fractals in maths, are infinite but can be described. Each small part looks like the whole, but the whole can never be fully known within a finite universe. Is that "potential" or "actual" infinity?

I've been thinking a lot about infinity this past week, mostly because of Conway's lectures. I'm trying to figure out whether the following logic makes sense.

- Assuming that the universe is finite -> Infinity cannot be approximated with finite numbers (MIP* = RE) [1] -> Numbers cannot have infinite strings of digits -> The future can never be perfectly preordained (Gisin) [2] -> Free will exists (Conway) [3]

This is not a proof that free will exists! But I think this is a consistency proof that free will is finite.

Now you're telling me that there's another kind of infinity, and I want to know what that means for this thought.

[1] https://www.quantamagazine.org/landmark-computer-science-pro...

[2] https://www.quantamagazine.org/does-time-really-flow-new-clu...

[3] https://www.youtube.com/watch?v=tmx2tpcdKZY&feature=youtu.be...

Free will is a philosophical concept which is essentially dualist. It's an attempt to reconcile two subjective experiences - the feeling of making a decision, and the fact that sometimes we can't predict the actions of others - with universal determinism.

There's no reason why universal determinism and free will need to be related. So trying to "prove" free will with math makes as much sense as "proving" free will with weather forecasting.

Even if that weren't true you still can't get to Conway's Step 3, because "free will" could just be statistical noise, and not willed in any sense at all.

>Free will is a philosophical concept which is essentially dualist.

Is it though? I came to the conclusion that one could consider free will the self-realization of a person in space-time -- in other words, free will is the only and only choice one can make (at each decision they face), that they make because of who they are thus far.

In that sense, "free will" is the same as the "person" (or the person's essense) -- and would it make sense for it to be any other way? Randomness wouldn't be free will, and having a second entity (e.g. a soul in dualism) do the decision making just moves the question and degree upwards (from "how the person has free will?" to "how the person's soul has free will?")

If a person faced with a choice A or B could go either way, then I wouldn't call that really free will (even though for some reason that's what most people have in mind when talking about the subject).

Either a person is a concrete personality/being and that manifests through its choices (which means that when faced with the A or B dillema they can only chose one or the other based on who they are), or they have some degree of randomness in their decision making (which makes them less of a person in my eyes -- randomness is not tied to our person, it is, as the name reveals, random).

When some people say "free will" they actually mean "free (independent) from the person". But that's not a will then -- a will denotes something being tied to a person (a person is their will).

You're conflating different kinds of randomness here.

A coin flip and a hand of cards are both random, but obviously cards are 'more random'.

This can be quantified - 'more random' is information complexity, or information entropy. (Two names for the same thing.)

If free will exists, then it must necessarily be a singularity of infinite information complexity, which is the same thing as a singularity of infinite randomness.

> Free will is a philosophical concept which is essentially dualist.

It's not, although many people think this. Consider that the majority of philosophers are actually Compatibilists, in which free will is compatible with determinism, and so they would disagree with your definition. If the majority of practicing experts disagrees with your view on their subject, it's probably time to revise your view.

First, I would take strong issue at your describing the majority of philosophers as Compatiblists. I can find no support for such a broad statement. Also, one of the primary criticisms of Compatiblism, dating back as early as Kant, is that what Compatibilists define as ‘free will’ is not free will as most people, including philosophers understand it. Pulling a quick quote, the Compatibilist position can typically expressed by the following:

Arthur Schopenhauer famously said, "Man can do what he wills but he cannot will what he wills." In other words, although an agent may often be free to act according to a motive, the nature of that motive is determined.

This position that the ‘free will’ people experience is the ability to ‘decide’ to take some and then take it, while then saying the the decision to do so was predetermined, is not what is meant (especially in the vernacular) by free will.

Therefore, while I will not support a metaphysical dualist basis for ‘free will’ it is clearly incorrect to dismiss an argument of such based on 1) an appeal to authority which is unsupportable (in that your claim about the position of a majority of ‘experts’ seems unsupported), and 2) that even if it was supported, that said appeal to authority is a valid refutation of an argument. Further, dismissal of an argument by choosing to substitute a contested definitional term (the meaning of free will) for one that is clearly not the same is not rhetorically valid.

> First, I would take strong issue at your describing the majority of philosophers as Compatiblists. I can find no support for such a broad statement

Almost 60% Compatibilist, the remainder evenly split among three other options: https://philpapers.org/surveys/results.pl

> Arthur Schopenhauer famously said, "Man can do what he wills but he cannot will what he wills." In other words, although an agent may often be free to act according to a motive, the nature of that motive is determined.

You're assuming this is relevant. Turns out, it's not.

> Also, one of the primary criticisms of Compatiblism, dating back as early as Kant, is that what Compatibilists define as ‘free will’ is not free will as most people, including philosophers understand it.

Nobody definitively understands free will. Some people conjecture it has certain properties, mainly incompatibilists. So far they have mostly been wrong.

> This position that the ‘free will’ people experience is the ability to ‘decide’ to take some and then take it, while then saying the the decision to do so was predetermined, is not what is meant (especially in the vernacular) by free will.

Experimental philosohy suggests pretty definitively that people's moral reasoning agrees with Compatibilism: https://www.researchgate.net/publication/274892120_Why_Compa...

> that even if it was supported, that said appeal to authority is a valid refutation of an argument.

The other poster provided no argument, they just made an unsupported claim.

The video timestamp you linked does not say "free will exists". Is says "humans has free will implies element particles have free will".

His definition of free will is quite limited. He only suggests that free will is limited to a "free" choice between options within one's power.

Conway said that there either is determinism or free will. If the future can be perfectly preordained (Gisin) due to infinite possibilities, then there is no free will. But if there are finite options, I think that there is "free will" for particles and people to choose between those options.

https://youtu.be/tmx2tpcdKZY?t=1074

https://en.wikipedia.org/wiki/Free_will_theorem

While there is technically no proof, there is a lot of evidence that the universe is infinite. In particular it's curvature is flat within the margin of measurement error which implies an infinite universe outside the observable universe.

"Actual infinity" is merely an abstraction, not unlike many others. It is very useful. Abstract thinking is part of what separates humans from (other) animals.

Potential infinities are just saying, you don’t have an infinity in your hand — you just have a recipe for arbitrarily large numbers (or arbitrary accuracy on real numbers, etc).

Eg, the “natural numbers” are a recipe to make as many as you want (by taking the successor of the last one) but not an actual (as in existing) infinite collection — the only ones which exist are the ones you construct, and the “potential infinity” refers to the fact that you can always make a new one.

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